arXiv subjects

Noah Kaufmann

Publications and source records attributed to Noah Kaufmann.

6 recordsLinked to original sources

arXiv2026

Entanglement Enhanced Sensing with Qubits affected by non-Markovian Dephasing

Entanglement has been proposed as a means to improve the sensitivity of sensing weak signals. While the degree of this quantum advantage is well understood in noiseless settings, the situation is more complex under realistic conditions, where the system is subject to decoherence. In this case, the enhancement depends on the specific noise characteristics. Previous treatments of colored noise typically assume that the noise is uncorrelated between successive experiments. Here, we consider the scenario in which the noise exhibits correlations across multiple shots. We derive a simple fundamental limit to the sensitivity based on the fact that the sensitivity cannot be better than the signal-to-noise ratio seen by the probe. Focusing on Ramsey spectroscopy with probes affected by pure classical dephasing, we show that, for suitable spatial and temporal noise correlations, entangled probes achieve a better scaling of the sensitivity with the number of probes than separable states. This demonstrates that entanglement can provide a substantial improvement for Ramsey spectroscopy subject to correlated noise.

quant-ph↗

arXiv2025

Estimating Bell Diagonal states with separable measurements

Quantum network protocols depend on the availability of shared entanglement. Given that entanglement generation and distribution are affected by noise, characterization of the shared entangled states is essential to bound the errors of the protocols. This work analyzes the estimation of Bell diagonal states within quantum networks, where operations are limited to local actions and classical communication. We demonstrate the advantages of Bayesian mean estimation over direct inversion and maximum-likelihood estimation, providing analytical expressions for estimation risk and supporting our findings with numerical simulations.

quant-ph↗

arXiv2025

Characterization of coherent errors in gate layers with robustness to Pauli noise

Characterization of quantum devices generates insights into their sources of disturbances. State-of-the-art characterization protocols often focus on incoherent noise and eliminate coherent errors when using Pauli or Clifford twirling techniques. This approach biases the structure of the effective noise and adds a circuit and sampling overhead. We motivate the extension of an incoherent local Pauli noise model to coherent errors and present a practical characterization protocol for an arbitrary gate layer. Notably, the coherent noise estimation is robust to Pauli noise. We demonstrate our protocol on a superconducting hardware platform and identify the leading coherent errors. To verify the characterized noise structure, we mitigate its coherent and incoherent components using a gate-level coherent noise mitigation scheme in conjunction with probabilistic error cancellation. The proposed characterization procedure opens up possibilities for device calibration, hardware development, and improvement of error mitigation and correction techniques.

quant-ph↗

arXiv2023

A Diamond Structure in the Transducer Hierarchy

We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which can be realized by a finite state transducer, which form an order based on which words can be transformed into other words. We provide a construction which proves the existence of a diamond structure, while also introducing a new function on streams which may be useful for proving more results about the transducer hierarchy.

cs.FL↗

arXiv2021

Classifying All Degrees Below $N^3$

We answer an open question in the theory of transducer degrees initially posed in [3], on the structure of polynomial transducer degrees, in particular the question of what degrees, if any, lie below the degree of $n^3$. Transducer degrees are the equivalence classes formed by word transformations which can be realized by a finite-state transducer. While there are no general techniques to tell if a word $w_1$ can be transformed into $w_2$ via an FST, the work of Endrullis et al. in [2] provides a test for the class of spiralling functions, which includes all polynomials. We classify fully the degrees of all cubic polynomials which are below $n^3$, and many of the methods can also be used to classify the degrees of polynomials of higher orders.

cs.FL↗

arXiv2021

A Diamond Structure in the Transducer Hierarchy

We answer an open question in the theory of transducer degrees on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which can be realized by a finite state transducer, which form an order based on which words can be transformed into other words. We provide a construction which proves the existence of a diamond structure, while also introducing a new function on streams which may be useful for proving more results about the transducer hierarchy.

cs.FL↗